In the late 1970s Thurston constructed hyperbolic metrics on most 3-manifolds which fiber over the circle. Around the same time, Feigenbaum discovered universal properties of period doubling, and offered an explanation in terms of renormalization. Recently Sullivan established the convergence of renormalization for real quadratic mappings.

In this work we present a parallel approach to renormalization and to the geometrization of 3-manifolds which fiber over the circle. This analogy extends the dictionary between rational maps and Kleinian groups; some of the new entries are included in Table 1.1.

Both discussions revolve around the construction of a nonlinear dynamical system which

EP - 10 PB - Princeton University Press PY - 1996 SN - 9780691011530 SP - 1 T2 - Renormalization and 3-Manifolds Which Fiber over the Circle (AM-142) UR - http://www.jstor.org/stable/j.ctt7ztfmd.3 Y2 - 2021/09/20/ ER -